# Ehrenfest Theorem for a Linear Potential

Classical Mechanics Level pending

Consider the quantum-mechanical wavefunction of a particle of mass $$m$$ moving in a linear potential

$V = \alpha x.$

The (normalized) wavefunction at $$t=0$$ is

$\psi(x) = \pi^{-1/4} e^{-x^2/2}.$

Find $$\langle x\rangle$$ as a function of time.

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